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Information × Registration Number 0115U007253, ( 0220U103925  ) R & D request Title Development of investigation methods of structures on manifolds associated with groups, algebras and graphs and development it geometric analysis concerning the theory of relativistic fields and particles. Head Mykytyuk Ihor V., Доктор фізико-математичних наукPelykh Volodymyr O., Доктор фізико-математичних наук Registration Date 12-01-2016 Organization Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine popup.description1 The aim of the research work is to create new methods for constructing and investigating invariant structures on cotangent bundles of homogeneous manifolds of compact groups and on the orbits of a cohomogeneous representation of complex Lie algebras, studying the representation of graphs on a plane and the topological and geometric structures associated with graphs and hypergraphs, construction Kirk-Livingstone finite-order invariants of classical plexuses, development of the method of integral manifolds for the investigation of multi-step singularly disturbed differential equations, the splitting of the linear system and the decomposition of nonlinear singularly perturbed differential equations with many time parameters, the development of the theory of column-string noncommutative determinants and the finding of generalized-inverse solutions of matrix and differential matrix equations; -the study of approximation properties of multidimensional continuous fractions and their application to the approximation of functions of many variables, development of methods of geometric analysis concerning the problem of behavior of solutions of Dirac equations, Sen-Witten, Maxwell and Matisson-Papapetrou equations in algebraically special and asymptotically flat Riemannian spaces, -development of numerical and analytical methods for constructing and studying the equations of evolution of a turbulent component of a magnetic field and its interaction with relativistic charged particles accelerated on shock waves in remnants of supernovae popup.nrat_date 2024-12-10 Close